Volume 47, Number 3, May-June 2013
|Page(s)||635 - 662|
|Published online||29 March 2013|
Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification∗
Division of Applied Mathematics, Brown University,
Providence, RI, 02912, USA
2 Lefschetz Center for Dynamical Systems, Division of Applied Mathematics,Brown University, Providence, RI, 02912, USA
Received: 22 March 2011
Revised: 13 March 2012
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we obtain explicit bounds on standard performance measures (variances, exceedance probabilities) over families of distributions whose distance from a nominal distribution is measured by relative entropy. The evaluation of the risk-sensitive expectations is based on polynomial chaos expansions, which help keep the computational aspects tractable.
Mathematics Subject Classification: 41A10 / 60H35 / 65C30 / 65C50
Key words: Epistemic uncertainty / aleatoric uncertainty / generalized polynomial chaos / relative entropy / uncertainty quantification / spectral methods / stochastic differential equations / monte Carlo integration / stochastic collocation method / quadrature
© EDP Sciences, SMAI, 2013
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